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The complexity of Fiber Bragg Grating (FBG) structures continually increases, for example in non-linear chirped FBGs for tunable dispersion compensation, dispersion-free FBGs in the DWDM networks, multi-channel sampled FBGs, DFB fiber lasers, gain-flattening filters (GFF) in Erbium doped fiber amplifiers (EDFAs), and other FBG applications.
There are applications in which it is desired to make FBGs with multiple bands of reflectivity in the telecommunications band around 1,550 nm, for example a band of reflectivity 1 nanometer wide at 1,550 nm, and then another at 1,552 nm. These periodically extend for example throughout the C-Band from about 1,530 nm to 1,565 nm, in which the erbium doped fiber amplifier has gain. The ITU standard grid either at 100 gigahertz spacing (roughly 0.8 nm), or 50 gigahertz spacing (roughly 0.4 nanometers) is where typical telecommunication laser transmitters operate that send voice and data information over telephone systems today. A standard set of frequencies or wavelengths in this 1,535 nm to 1,565 nm band has been selected by standards committees, and it is therefore of interest to fabricate FBGs which operate at those wavelengths. In such an FBG there is an underlying grating period of about 0.5 micron with slower superimposed modulations that produce effects like chirp and non-linear chirp, which are fundamentally important to particular applications such as dispersion compensation.
The reflectivity peak of a Bragg grating occurs at a wavelength equal to twice the index of refraction of the fiber core times the physical period of the index grating. Typically, the period of the index grating is about 0.5 micron and the index of refraction is about 1.5, such that twice 1.5 times 0.5 microns results in 1.5 microns or reflectivity in the band around 1500-1550 nanometers.
One approach is to make a fiber Bragg grating that, rather than reflecting in a wide continuous wavelength band which can result in a FBG which is impractically long, reflects specifically in multiple channels located at periodically spaced frequencies (or wavelengths). Each channel reflects in a certain bandwidth around its central wavelength, and in this bandwidth the FBG can provide a number of filtering functions, such as tunable dispersion compensation. A method called sampling imposes a periodic superstructure on the underlying 0.5 micron basic Bragg grating period, producing a multiplicity of Bragg reflection peaks in the spectrum surrounding the underlying Bragg reflection wavelength. The superstructure can be understood in terms of a Fourier transform argument. The underlying grating reflects at a certain wavelength, and the imposed superstructure has a Fourier transform which represents a comb function of regularly spaced peaks, one for each channel, and having a certain envelope that determines the spectral distribution or uniformity of the reflectivities of those channels. It is sufficient to understand that the multiplicity of channels is determined by the Fourier spectrum of the periodic superstructure, which can periodically vary the underlying FBG either in phase, i.e. the locations of the index modulations, or amplitude, i.e. the magnitude of the index modulations. The period of such a superstructure can be about a millimeter to generate channels with a 100 gigahertz spacing in the telecommunications band, much longer than the fundamental 0.5 micron structure of the grating.
To write a grating of periodic index variation in the core of a fiber, one way is to propagate UV light into that core. Where the UV light exposes the core, the index of refraction increases slightly, and where it does not, it does not change at all. If the basic exposure pattern has a period of about 0.5 microns, that will create reflectivity in the telecommunications band around 1,500 nanometers.
A phase mask is widely used in manufacturing fiber Bragg gratings (FBG). The side-writing systems using phase masks in close proximity to the fiber are less critical to alignment, vibration and UV beam coherence than are imaging or holographic direct write systems that demand interferometric accuracies. Accordingly, phase masks are particularly suitable for industrial fabrication. In addition, the nanometer scale structures required by the FBG are built into the phase mask, benefiting from high accuracy lithographic mask technology.
In prior art side-writing technology a fiber is placed as close as possible to the mask, which is a slab having a periodically varying surface grooves. When UV light propagates through the mask, it splits into multiple diffraction orders. The mask is manufactured such that the zeroth diffraction order, which ordinarily goes straight through, is suppressed, for example by a standard technique of adjusting the depth of the grooves in the mask. The groove depth is chosen for a particular mask groove period, such that the zeroth order is suppressed. The FBG is formed from the interference between the plus first and minus first orders diffracted from the phase mask. About 35 per cent to 40 per cent of the incident light is diffracted by the mask into each of the plus and minus first orders. Higher diffraction orders typically do not contribute to formation of the relevant Bragg index modulation in the fiber and are thus ignored, and in some circumstances are eliminated by inserting additional optics.
The interference between the two UV beams diffracted from the mask creates an intensity modulation in the core of the fiber, which modulates the index in the photosensitive fiber core. The UV writing beam may have a wavelength of typically around 244 nanometers, although the method may be used at any wavelength at which the fiber exhibits sufficient photosensitivity. For FBGs in the 1550 nm telecommunication band, the period of the mask is selected to be about 1070 nm, which produces an angle of diffraction of the first order beams of roughly +/xe2x88x9213 degrees, so that the two diffracted beams propagate at 26 degrees with respect to each other. When two beams are at 26 degrees to each other, they create an intensity interference pattern with a 535 nm basic period, which then generates a Bragg reflection in the band around 1550 nm. This side writing method is the standard prior art that many FBG manufacturers use, e.g. see U.S. Pat. No. 5,367,588, issued Nov. 22, 1994.
Additionally, prior art U.S. Pat. No. 6,081,640, issued Jun. 27, 2000, describes a periodic superstructure that can be either in phase, amplitude, pitch of the grating, anything that varies periodically and is recognized to create multiple channels, but does not disclose in detail how to incorporate variation of pitch or phase. One method described in U.S. Pat. No. 6,081,640 uses amplitude sampling, in which the mask has a periodic amplitude superstructure. To create a large number of reflective channels using amplitude sampling requires a very small duty factor. That is, for example, a periodic rectangular wave amplitude superstructure pattern where the xe2x80x9conxe2x80x9d section is extremely short and the xe2x80x9coffxe2x80x9d section is very long, generates many channels, but that periodic superstructure is xe2x80x9coffxe2x80x9d most of the time, such that there is no grating in most of the fiber. That is, a small section of grating is followed by a long section with no grating present, which is then is followed by another small section of grating. To achieve significant reflectivity the light must interact for a reasonably long path length with the grating. The way Bragg reflection works is that each reflection from a single period of index variation is extremely small, on the order of 10xe2x88x923 reflection amplitude from each index period, and at the Bragg resonance wavelength they add constructively to generate a high reflectivity band.
Therefore, amplitude sampling is extremely inefficient, since most of the fiber has no grating present. In contrast, phase sampling, i.e., periodically varying either the pitch or equivalently the phase of the grating, creates multiple channels without turning off the grating. Consequently, light is always interacting with the periodic grating modulation along the entire length of the FBG, and it can be more efficient by approximately the square root of the number of channels in using the amplitude of the index grating in the fiber.
Phase-steps are examples of basic structures in a variety of FBGs, which introduce phase shifts in the FBG profile function. To write phase-steps in the FBG, a widely used method is to incorporate phase-steps of the same sizes and at the same locations along the fiber in the phase mask. This approach was first proposed by R. Kashyap et al., xe2x80x9cUV written reflection grating structures in photosensitive optical fibers using phase-shifted phase masks,xe2x80x9d Electron. Lett. Vol. 30, p. 1977-1978 (1994), followed by many laboratories across the world (see for example R. Kashyap, xe2x80x9cFiber Bragg gratings,xe2x80x9d Chapter 6 (Academic Press, San Diego, p. 227-309 (1999)), because the preliminary experiments showed that the phase-step in the phase-shifted phase mask is substantially replicated in the FBG. However, J. A. R. Williams et al. in xe2x80x9cThe Effects of Phase Steps in E-Beam Written Phase Masks Used for Fiber Grating Fabrication by Near-Field Holography,xe2x80x9d ECOC 97, 187-190 (1997), reported experimental results, which showed disparity from those predicted by the phase-step replication model. Using the Fresnel-Kirchoff diffraction equations, they calculated the phase mask interference pattern at the fiber core, and the FBG spectrum. The numerical results showed asymmetry in the FBG spectrum, which is not predicted by the replication model.
Therefore, what is needed in the art are a system and method for writing efficient multi-channel FBG gratings using a phase mask, such that the generated FBG spectrum accurately reproduces the intended design substantially free of asymmetry.
The present invention is directed to a system and method for designing efficient multi-channel FBG gratings using a pre-compensated phase mask for diffracting light for side-writing the grating on an optical fiber core. In accordance with embodiments of the present invention, a desired phase function of the FBG is generated, specifically tailored to an effective spacing between the phase mask and the optical fiber core. From the phase function a phase mask is pre-compensated to offset diffraction effects associated with each longitudinal position of the FBG receiving light primarily from two corresponding longitudinal positions of the phase mask that are substantially symmetrically spaced longitudinally relative to each particular longitudinal position of the FBG. The two corresponding longitudinal positions of the phase mask are spaced apart from each other with a longitudinal spacing determined by the effective spacing between the phase mask and fiber core and by the first order diffraction angle of light through the phase mask. The embodiments of the present invention generate a FBG spectrum that accurately reproduces the intended design, where the effect of the diffraction of the writing beam from the mask to the proximally located fiber is properly accounted for.
In a first embodiment, a continuous phase variation is to be imparted to the FBG. It is disclosed that the phase imparted to the FBG is substantially given by the sum of the phases of the mask corrugation at two separate locations on the mask, symmetrically spaced longitudinally relative to the position in the FBG. Based on this understanding, it is shown that the fraction effects can be accounted for by pre-compensation of the phase function on the mask. In this approach Fourier filtering of the desired FBG phase function with the inverse of the spatial frequency transfer function of diffraction effect, gives a mask function that will generate the desired FBG phase function, after including the effects of diffraction.
In further embodiment, an FBG design approach disclosed in U.S. patent application Ser. No. 09/757,386, the disclosure of which has been incorporated herein by reference, uses a concept called xe2x80x98the Dammann grating.xe2x80x99 This type of grating is a periodic sequence of discrete xcex1 phase shifts at locations, optimized so that the Fourier spectrum of the pattern is a set of equally spaced channels with a desired overall envelope (see for example J. N. Mait, xe2x80x9cDesign Of Binary Phase and Multi-Phase Fourier Gratings for Array Generation,xe2x80x9d Journal of the Optical Society of America A, Vol. 7, (1990) p. 1514-1528). Phase steps on the phase mask constitute the key structure in this approach to a multichannel sampled FBG. Numerical analysis shows that the phase steps on the phase mask are not replicated in the fiber core in the contact side-writing process, as asserted by Kashyap et al., Electron. Lett. (1994), cited above. Instead, because of free space propagation from phase mask to the fiber core, a phase step on the phase mask becomes divided into two equal phase steps in the FBG, which are separated by a distance proportional to the spacing between phase mask and fiber core. As a consequence of this phase step separation, the envelope of the multiple spectral channels, which are created by the sampling function in the FBG, will be modulated by a cosine envelope, which is shifted by xcfx80/4 in phase with respect to the central wavelength of the envelope.
The present invention disclosure demonstrates by using a rigorous Finite Difference in Time Domain (FDTD) method that a phase-step in the phase-shifted phase mask is not replicated in the fiber core, but is split into two equal phase-steps by beam diffraction, generating an asymmetric distortion of the multi-channel FBG spectrum. A theoretical model relates the experimental asymmetry in the FBG spectrum to the splitting of the phase-steps. Alternating the signs of the xcfx80/2 phase-steps in the phase mask recovers the symmetry of the FBG structure in spite of the phase-step splitting. A series of new phase mask design methods take into account the splitting of the phase-steps and eliminates the asymmetric distortion of the multi-channel FBG spectra.
Embodiments of the invention disclose a fundamental understanding of diffraction of the phase mask, which can be applied to the most widely used FBG fabrication process and to substantially all designs of phase-shift phase masks used for contact side-writing of superstructure FBGs.